Influence functions of trimmed likelihood estimators for lifetime experiments

Abstract

We provide a general approach for deriving the influence function for trimmed likelihood estimators using the implicit function theorem. The approach is applied to lifetime models with exponential or lognormal distributions possessing a linear or nonlinear link function. A side result is that the functional form of the trimmed estimator for location and linear regression used by Bednarski and Clarke (1993, 2002) and Bednarski et al. (2010) is not generally always the correct functional form of a trimmed likelihood estimator. However, it is a version for which the influence function has a treatable form. A real data example shows the effect of trimming using a nonlinear link function for either the exponential or lognormal distribution.